Finite Group Databasebeta

← #49133170

Subgroups — #49133170

Order 36224.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827165C211yesmaximal, characteristic, complemented
2#31827123C211yesmaximal, characteristic, complemented
3#31826819C211yesmaximal, characteristic, complemented
4#31826805C211yesmaximal, characteristic, complemented
5#31826782C211yesmaximal, characteristic, complemented
6#31826773C211yesmaximal, characteristic, complemented
7#31826698C211yesmaximal, characteristic, complemented
8#31826691C211yesmaximal, characteristic, complemented
9#31826607C211yesmaximal, characteristic, complemented
10#31826602C211yesmaximal, characteristic, complemented
11C4×#17985380C211yesmaximal, characteristic, complemented
12#31826530C211yesmaximal, characteristic, complemented
13#31826458C211yesmaximal, characteristic, complemented
14#103×D283C211yesmaximal, characteristic, complemented
15#463×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C2×Q8×D283C2211yescharacteristic
18C2×#17985380C2211yescharacteristic
19C2×C8×D283C2211yescharacteristic
20C2×C8×D283C2211yescharacteristic
21#22583603—21no—
22#22583602C2211yescharacteristic
23#22583596—21no—
24#22583593—21no—
25#22583587—21no—
26#22583586C2211yescharacteristic
27#22583583—21no—
28#22583583—21no—
29#22583581C2211yescharacteristic
30#22583581C2211yescharacteristic
31#22583581C2211yescharacteristic
32C4×Dic566C2211yescharacteristic
33C4×D1132C2211yescharacteristic
34C4×C22⋊D283—21no—
35(C22⋊D283)⋊C4—21no—
36#22583568C2211yescharacteristic
37C4⋊C4×D283C2211yescharacteristic
38#22583544C2211yescharacteristic
39#22583542C2211yescharacteristic
40#22583541C2211yescharacteristic
41#22583535C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583534C2211yescharacteristic
44#22583534C2211yescharacteristic
45#22583533C2211yescharacteristic
46#22583531C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583531C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51C4×C283⋊C8C2211yescharacteristic
52C2×SD16×C283C2211yescharacteristic
53C2×D8×C283C2211yescharacteristic
54#124×C283C2211yescharacteristic
55C4×D4×C283C2211yescharacteristic
56C4⋊C8×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59#17985391—22no—
60#17985391—41no—
61C2×Dic566—21no—
62C2×Dic566C2311yescharacteristic
63Q8×D283—22no—
64Q8×D283—41no—
65C2×D1132D411yescharacteristic
66C2×C22⋊D283—21no—
67C2×C22⋊D283—21no—
68C2×C22⋊D283—21no—
69C2×C22⋊D283—21no—
70C22×Dic283—21no—
71C2×C4×D283—21no—
72C2×C4×D283—21no—
73C2×C4×D283C2311yescharacteristic
74C2×C4×D283C2311yescharacteristic
75#17985380—22no—
76C2×C283⋊C8C2311yescharacteristic
77C2×C283⋊C8C2311yescharacteristic
78C8×D283—41no—
79C8×D283—41no—
80C4⋊Dic283D411yescharacteristic
81C4⋊Dic283C2311yescharacteristic
82C4⋊Dic283C2311yescharacteristic
83C4⋊Dic283C2311yescharacteristic
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89C22⋊Dic283—21no—
90C22⋊Dic283—21no—
91C22⋊Dic283—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4D411yescharacteristic
95(C2×D283)⋊C4D411yescharacteristic
96C4×Dic283—21no—
97C4×Dic283—21no—
98C2×Q8×C283C2311yescharacteristic
99C2×D4×C283C2311yescharacteristic
100C2×D4×C283C2311yescharacteristic
101C22×C4×C283—21no—
102SD16×C283—41no—
103D8×C283—41no—
104C2×C8×C283C2311yescharacteristic
105C2×C8×C283C2311yescharacteristic
106C4⋊C4×C283C2311yescharacteristic
107C22⋊C4×C283—21no—
108C22⋊C4×C283—21no—
109C22⋊C4×C283—21no—
110C42×C283C2311yescharacteristic
111C22×D283C2×D411yescharacteristic
112C22×D283C2×D411yescharacteristic
113Dic566—21no—
114Dic566—42no—
115Dic566#4112yes—
116D1132—22no—
117C22⋊D283—42no—
118C22⋊D283—42no—
119C22⋊D283—42no—
120C22⋊D283—81no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283—42no—
126C2×Dic283C2×D411yescharacteristic
127C2×Dic283C2×D411yescharacteristic
128C4×D283—21no—
129C4×D283—21no—
130C4×D283—21no—
131C4×D283—21no—
132C4×D283—42no—
133C4×D283—81no—
134C283⋊C8—21no—
135C283⋊C8—21no—
136C23×C283—21no—
137C23×C283—21no—
138Q8×C283—21no—
139Q8×C283—21no—
140D4×C283—21no—
141D4×C283—21no—
142D4×C283—21no—
143D4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—81no—
147C2×C4×C283C2×D411yescharacteristic
148C2×C4×C283C2×D411yescharacteristic
149C2×C4×C283C2411yescharacteristic
150C8×C283—21no—
151C8×C283—21no—
152C22×C283—41no—
153C22×C283—41no—
154C22×C283—41no—
155C22×C283—41no—
156C22×C283—41no—
157C22×C283—41no—
158C22×C283C22×D411yescharacteristic
159C2×D283—21no—
160C2×D283—21no—
161C2×D283—21no—
162C2×D283—21no—
163C2×D283—21no—
164C2×D283#13512yes—
165C4×C283—21no—
166C4×C283—21no—
167C4×C283—41no—
168C4×C283—41no—
169C4×C283C2×#4111yescharacteristic
170C4×C283H(5,𝔽2)11yescharacteristic
171Dic283—21no—
172Dic283—21no—
173Dic283—22no—
174Dic283—41no—
175Dic283—41no—
176Dic283—41no—
177C2×C283—81no—
178C2×C283—81no—
179C2×C283#54611yescharacteristic
180C2×C283C2×#13511yescharacteristic
181C2×C283#57711yescharacteristic
182D283—22no—
183D283—41no—
184C283#330111yescharacteristic, complemented, Sylow
185#3301—2831nomaximal, Sylow
186#553—2831no—
187#548—2831no—
188#488—2831no—
189#485—2831no—
190#481—2831no—
191#479—2831no—
192#466—2831no—
193#465—2831no—
194#463D28311yescharacteristic, complemented
195#449—2831no—
196#448—2831no—
197C4×SD16—2831no—
198C8×D4—2831no—
199#416—2831no—
200C2×#103—2831no—
201C2×#41—2831no—
202C22×Q8—2831no—
203C2×SD16—2831no—
204C2×SD16C2×D28311yescharacteristic
205C2×D8C2×D28311yescharacteristic
206C22×C8—2831no—
207C22×C8—2831no—
208#126—5661no—
209#125—2831no—
210#124—5661no—
211#124C2×D28311yescharacteristic
212#123—5661no—
213C22⋊Q8—2831no—
214C22⋊Q8—5661no—
215#121—2831no—
216#121—2831no—
217#121—2831no—
218#121—5661no—
219#121—5661no—
220C4×Q8—2831no—
221C4×D4—2831no—
222C4×D4—5661no—
223C4×D4—5661no—
224C4×D4C2×D28311yescharacteristic
225#117—2831no—
226C2×C4⋊C4—2831no—
227#107—2831no—
228#106—2831no—
229#106—2831no—
230C4⋊C8C2×D28311yescharacteristic
231#103—2831no—
232#103—2831no—
233#103—2831no—
234#103—2831no—
235#103—2831no—
236#103C2×D28311yescharacteristic
237#102—2831no—
238#102—2831no—
239#102—2831no—
240#102C2×D28311yescharacteristic
241C22⋊C8—2831no—
242C22⋊C8—2831no—
243C4×C8—2831no—
244#41—5662no—
245#41—11321no—
246C2×Q8—2831no—
247C2×Q8—5661no—
248C2×Q8—5662no—
249C2×Q8—11321no—
250C2×Q8C22×D28311yescharacteristic
251C2×D4—2831no—
252C2×D4—5661no—
253C2×D4—5661no—
254C2×D4—5661no—
255C2×D4—5661no—
256C2×D4C22×D28311yescharacteristic
257C2×D4C22×D28311yescharacteristic
258C22×C4—21no—
259C22×C4—2831no—
260C22×C4—2831no—
261C22×C4—5661no—
262C22×C4—5661no—
263C22×C4—5661no—
264SD16—41no—
265SD16—5662no—
266D8—41no—
267C2×C8—2831no—
268C2×C8—2831no—
269C2×C8—11321no—
270C2×C8—11321no—
271C2×C8C22×D28311yescharacteristic
272C2×C8C22×D28311yescharacteristic
273C4⋊C4—2831no—
274C4⋊C4—2831no—
275C4⋊C4—2831no—
276C4⋊C4—2831no—
277C4⋊C4—5661no—
278C4⋊C4—5661no—
279C4⋊C4—5661no—
280C4⋊C4—5661no—
281C4⋊C4—5661no—
282C4⋊C4C22×D28311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—2831no—
287C22⋊C4—2831no—
288C22⋊C4—5661no—
289C22⋊C4—5661no—
290C22⋊C4—5661no—
291C22⋊C4—5661no—
292C22⋊C4—5661no—
293C42—5661no—
294C42—5661no—
295C42C22×D28311yescharacteristic
296C23—21no—
297C23—21no—
298C23—2831no—
299C23—2831no—
300Q8—21no—
301Q8—21no—
302Q8—2832no—
303Q8—5661no—
304Q8—11322no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—5662no—
310D4—11322no—
311D4—11322no—
312D4—11322no—
313D4—22641no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—81no—
317C2×C4—2831no—
318C2×C4—2831no—
319C2×C4—5661no—
320C2×C4—5661no—
321C2×C4—5661no—
322C2×C4—5661no—
323C2×C4—5661no—
324C2×C4—5661no—
325C2×C4—5661no—
326C2×C4—5661no—
327C2×C4—11322no—
328C2×C4—11322no—
329C2×C4—22641no—
330C2×C4D4×D28311yescharacteristic
331C2×C4D4×D28311yescharacteristic
332C2×C4C23×D28311yescharacteristic
333C8—21no—
334C8—21no—
335C8—5661no—
336C8—5661no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—2832no—
344C22—5661no—
345C22—5661no—
346C22—5661no—
347C22—5661no—
348C22—5661no—
349C22C2×D4×D28311yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—5661no—
355C4—5661no—
356C4—5662no—
357C4—11321no—
358C4—11321no—
359C4—11321no—
360C4#41×D28311yescharacteristic
361C4#2258365511yescharacteristic
362C2—81no—
363C2—81no—
364C2—5662no—
365C2—11321no—
366C2#3182711211yescharacteristic
367C2#135×D28311yescharacteristic
368C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#463×C283C2
socleC22×C283C22×D4
hypercenter#463D283
hypocenterC283#3301
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #31827165C2semidirect
2. #31827123C2semidirect
3. #31826819C2semidirect
4. #31826805C2semidirect
5. #31826782C2semidirect
6. #31826773C2semidirect
7. #31826698C2semidirect
8. #31826691C2semidirect
9. #31826607C2semidirect
10. #31826602C2semidirect
11. C4×#17985380C2semidirect
12. #31826530C2semidirect
13. #31826458C2semidirect
14. #103×D283C2semidirect
15. #463×C283C2semidirect
184. C283#3301semidirect
194. #463D283semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#318271652
#318271232
#318268192
#318268052
#318267822
#318267732
#318266982
#318266912
#318266072
#318266022
C4×#179853802
#318265302
#318264582
#103×D2832
#463×C2832
#3301283